Question: Emily is 3 times as old as Ashley. Twelve years ago, Emily was 7 times as old as Ashley. How old is Emily now?
Answer: We can use the given information to write down two equations that describe the ages of Emily and Ashley. Let Emily's current age be $e$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $e = 3a$ Twelve years ago, Emily was $e - 12$ years old, and Ashley was $a - 12$ years old. The information in the second sentence can be expressed in the following equation: $e - 12 = 7(a - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = e / 3$ . Substituting this into our second equation, we get: $e - 12 = 7($ $(e / 3)$ $- 12)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $e - 12 = \dfrac{7}{3} e - 84$ Solving for $e$ , we get: $\dfrac{4}{3} e = 72$ $e = \dfrac{3}{4} \cdot 72 = 54$.